There also exists an intent in the opposite way, especially after the work of Aharanov and Bohm [1]}, to think of \((\vec{A}, \phi )\)  as physical reality. Another support for this idea is that the Coulomb field always accompanies a charge, and can never be stripped away. We do not claim either that our findings add to that intent. In fact, we must be clear-minded that our starting point, namely the semi-classical Hamiltonian (REF ) or (REF ) under the external-field approximation, is known to be unsafe if the external source is relativistic [2]}, while a safe and fully quantum-field method is still lacking. In such a circumstance, the gauge-dependence we just found is not a disaster, but an advantage: Since the Hamiltonian (REF ) or (REF ) is not justified anyway, there is no sense in sticking to the actual \((\vec{A}, \phi )\)  generated by the external source. Instead, one may always try to define an effective external field which, when plugged into the Hamiltonian (REF ) or (REF ), may fit well the experimental data. This is indeed quite probable, as we saw that by just tuning the gauge, we may fit the peak frequency of the radiation spectrum; and another overall factor may be multiplied to fit the radiation intensity. Namely, the effective external field may likely be parameterized with the gauge potential in a particular gauge. This gauge is not necessarily among the most common ones, and might possibly be individualized condition for the field of each charge, instead of the usual conditions for the overall field.
